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How do you write the equation of the line given (8, -3) and (-2, 2)?

Answer 1

Kennedy Adams

#y=-1/2x+1#

#"the equation of a line in "color(blue)"slope-intercept form"# is.

#•color(white)(x)y=mx+b#

#"where m is the slope and b the y-intercept"#

#"to calculate m use the "color(blue)"gradient formula"#

#•color(white)(x)m=(y_2-y_1)/(x_2-x_1)#

#"let "(x_1,y_1)=(8,-3)" and "(x_2,y_2)=(-2,2)#

#rArrm=(2-(-3))/(-2-8)=5/(-10)=-1/2#

#rArry=-1/2x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute either of the 2 given points into "# #"the partial equation"#

#"using "(-2,2)" then"#

#2=1+brArrb=2-1=1#

#rArry=-1/2x+1larrcolor(red)"is the equation of the line"#

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Answer 2

Ethan Adkins

You can use the point-slope form of a linear equation: ( y - y_1 = m(x - x_1) ), where ( (x_1, y_1) ) is a point on the line and ( m ) is the slope. First, find the slope using the formula ( m = \frac{{y_2 - y_1}}{{x_2 - x_1}} ) with the given points. Then, choose one of the points and plug its coordinates and the slope into the point-slope form to get the equation of the line.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.